342A Gerofsky Lesson Plans I–II–III

Subject: Pre Calculus	Grade: 12	Date: 17 Dec.’17	Duration: 75 to 80 mins
Overview	All the lessons are based from the curriculum text: McGraw-Hill Ryerson Pre-Calculus 12 [pgs. 166 until 324] 15 or 16 pages roughly ought to be covered per day in this unit, for a total of 11 or 10 lessons Every lesson below performs within the new curriculum guidelines, however I.B.-DP content is present within this file
Class Profile	TEO, TBA

Big Idea(s)	Transformations of shapes extend to functions in all of their representations Analyzing the characteristics of functions allows us to solve equations, and model and understand relationships
Curriculum Competencies	Apply flexible strategies to solve problems in both abstract and contextualized situations Model mathematics in contextualized experiences Use mathematical vocabulary and language to contribute to mathematical discussions
Content	Transformations of functions, including (symbols not included) Trigonometric functions and equations with real numbers
Literacy Objectives	I  Investigating Sine & Cosine laws in triangles (with the hour and minute hand on a clock fixed at 3:15) while spinning counterclockwise II  Using the Desmos app, we show how transformations/translations in Trigonometry differ from polynomial functions. III  The final project, where groups investigate Sinusoidal word problems adapting the material taught

Materials and Equipment Needed for this Lesson

Pencil/pen Paper/notebook brought to class Protractor Graphing calculator (will be provided if necessary) Ruler

	Lesson Stages	What the teacher will be doing	What the students will be doing	Time
1	Warm-up	Hook I Let’s hold the time at 3:15, and spin backward (a clock will be provided for every student) Hook II We need to get a more accurate view of why whole number translations are different for polynomials than they are for Trigonometric ones.  Let’s see why Hook III If you were a navigator, and wanted to dock your ship safely, how could you be sure that happens?  We now know amplitudes, phase shifts, and behaviours of sinusoidal functions.	Spinning a non-active clock counterclockwise, discovering obtuse and acute triangles Whole numbers will be converted to radial numbers Use Desmos here Group project (1/2) = class time for research (2/2) = mini presentations	(15 mins) (15 mins) (15 mins)
2	Presentation	I So how does clock spinning relate to angles in a triangle? Remember, we have to connect where the hand counts seconds to the time 3:15 Do we get different triangles every time? And some of the time we don’t even get a triangle at all.  Why is that? II Let’s experiment with what it really means to “move” either the Sine or Cosine curve Left or Right If we take the approach of mapping notation, and compare it to what we did last class with the clocks, then x ~~> (x – π/2) would mean that we’re “moving” every point right by 90o If you brought your spinners today, try it out with the person sitting beside you and get practice converting degrees into radians III (1/2) So to get you started for the project, where can you find some real-world examples (maybe in the subjects of Physics or Music – we could have some students map height on a Ferris wheel.  A musical example would be oscillations in a given pitch) that “look” like a Sine or Cosine curve? Let’s come up with a mind map on the whiteboard here, and I would like you to get into groups of five (we should have around six clusters, presuming an enrollment of 30 students) If we can get everyone doing a separate and unique project, that would be great (2/2) N/A – presentations	If the seconds ticker falls on the 9, it’s merely a straight line	(20 mins) (20 mins) (20 mins)
3	Practice	I Using our protractors and rulers, link up your measurements with the Sine and Cosine laws Can we figure out why for the triangles you made using the clock, both laws work? II I want us to figure out ways/ possibilities for moving Sine and Cosine “around” our graphs here Please get your tablets out, and experiment! (through the Desmos app) What are you finding out when we substitute x ~~> (x – (π / a number)) or x ~~> (x + (π / a number))? Are brackets helpful?  Why or why not? III (1/2) Section devoted researching their particular topic/approach to a sinusoidal problem (2/2) Presentations given by my students		(30 mins) (30 mins) (30 mins)
4	Discussion	I Would anyone like to share their rationale for proving the Sine and Cosine law? What measurements did people from different tables discover their angles were? Was it consistent with what these laws said? II So what did you learn from experimenting with Desmos? That plus (+) and minus (–) some radian number can be tricky, but we just have to be careful, that’s all.  I think we should have a little more practice with it, because when we get to combining everything together, it can get confusing III (1/2) So could everyone get in touch with their group members tonight and inquire about amplitudes, phase shifts, and whether or not you choose to graph using a Sine or Cosine function (2/2) I really enjoyed all of the presentations guys!  What thoughtful ideas on how to connect sinusoidal patterns and behaviours to lifelike situations!		(10 mins) (10 mins) (10 mins)
5	Closure	I Well, we found new ways of demonstrating math connected in clocks, too! II Does everyone feel confident with the material we have just covered today?  Does anyone have a question? (first to five check) III (1/2) N/A – group collaboration (2/2) Can I get everyone to write on a small piece of paper (provided) what they thought of the experiment? Were you surprised at all in anything?		(4 mins) (4 mins) (4 mins)

Reflection:

Having a copy of McGraw-Hill Ryerson Pre-Calculus 12 is helpful, because now I know how to pace all of my lessons. And I believe it was helpful in figuring out what/how a Unit Plan should read, and I definitely will use the holidays for improving my clarity on some lessons